Stress constrained topology optimization with free-form design domains

This paper aims at dealing with realistic and challenging design problems of stress constrained topology optimization with free-form design domains. First, the concept of level set function (LSF) based modelers is introduced to transform this kind of problems into the Boolean conjunction operation of a topology variation modeler (TVM) onto a free-form design domain modeler (FDDM). Such an operation is mathematically realized by means of the so-called R-functions in the form of implicit LSFs. Within this framework, topology optimization problems are classified into two general cases depending upon the existence of non-designable solid feature. Analytical sensitivity analysis formulas are further derived. Compared with the existing level set based method, the important sensitivity property of design domain preserving makes it possible to avoid automatically the boundary violation of the design domain caused by the zero level set movement and both the topology and boundary shape of the free-form design domain can be simultaneously optimized. Second, the implementation of the finite cell method (FCM) ensures the stress computing accuracy in the fixed mesh due to the use of high-order shape functions and adaptive integration scheme. The combination of the active-set strategy and the dynamic aggregation technique also reduces the number of local stress constraints greatly. Finally, representative examples are presented to illustrate the conveniences and effectiveness of the proposed method.